Industrial Programming with Cut Constraints for Faster MIP Solving
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Industrial programming problems, such as factory production planning and resource scheduling, are complex and time-consuming due to large scales and numerous constraints, leading to inefficiencies in obtaining optimal solutions.
Innovation Solution
The method involves constructing a cut constraint associated with integer parameters in mixed integer programming (MIP) models, allowing for the conversion of constraints into a relaxation model without relying on conventional solving results, thereby improving solving quality and reducing computation costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional MIP solving methods are used, then optimal solutions can be obtained, but the solving process is time-consuming and computing-intensive
Solution Approach 1:
The patent applies preliminary action by constructing cut constraints before solving the MIP model. Specifically, Gomory cut constraints and other valid inequalities are pre-generated and added to the relaxation model before the main solving process begins. This preliminary preparation reduces the computational burden during the actual solving phase by eliminating fractional solutions in advance, thereby reducing solving time while maintaining solution optimality.
Solution Approach 2:
The patent uses relaxation models as intermediaries between the original MIP problem and the final optimal solution. By introducing relaxation models with added cut constraints, the method creates an intermediate solving stage that provides tighter bounds and guides the search toward optimal integer solutions more efficiently, reducing both time and computational requirements.
2Adaptability or versatility
If the scale of industrial programming problems increases, then more comprehensive solutions can be obtained, but computation costs increase significantly
Solution Approach 1:
The patent applies segmentation by dividing the constraint construction process into distinct stages: generating Gomory cut constraints, generating other valid inequalities, and combining them into a comprehensive relaxation model. This segmented approach allows the system to handle large-scale problems by processing constraints in manageable stages, reducing memory requirements and computation costs while maintaining the ability to solve comprehensive industrial programming problems.
Solution Approach 2:
The patent changes parameters by transforming the original MIP constraints into a relaxation model with modified constraint types. By converting integer constraints into relaxed constraints with added cut inequalities, the method changes the parameter types and constraint structures, enabling the solution of larger problems with reduced computational intensity while preserving the essential problem characteristics.
3Speed
If relaxation models are constructed without cut constraints, then solving speed may be faster, but solution quality deteriorates
Solution Approach 1:
The patent applies partial action by selectively adding only the most effective cut constraints to the relaxation model. Rather than adding all possible constraints, the method generates Gomory cuts and other valid inequalities that provide the greatest improvement in solution quality with minimal computational overhead. This partial addition of constraints maintains solving speed while significantly improving solution quality compared to unconstrained relaxation models.
Data Source
AI summary
An industrial programming method and apparatus, a device, a storage medium, and a program product are provided. In a programming scheme generation method, a programming device obtains a first group of constraints for a plurality of parameters in an industrial programming job. Further, the programming device constructs, based on the first group of constraints, a cut constraint associated with at least one integer parameter in the plurality of parameters, and constructs a second group of constraints based on the cut constraint and the first group of constraints, where a type of the at least one integer parameter in the second group of constraints is changed. The programming device determines values of the plurality of parameters based on the second group of constraints, to generate a programming scheme for the industrial programming job.